Is ${970814}$ divisible by $4$ ?
Solution: A number is divisible by $4$ if the last two digits are divisible by $4$ . [ Why? We can rewrite the number as a multiple of $100$ plus the last two digits: $ \gray{9708} {14} = \gray{9708} \gray{00} + {14} $ Because $970800$ is a multiple of $100$ , it is also a multiple of $4$ So as long as the value of the last two digits, ${14}$ , is divisible by $4$ , the original number must also be divisible by $4$ Is the value of the last two digits, $14$ , divisible by $4$ No, $14$ is not divisible by $4$, so $970814$ is also not divisible by $4$.